Free Statistics

of Irreproducible Research!

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_centraltendency.wasp
Title produced by softwareCentral Tendency
Date of computationMon, 20 Dec 2010 12:30:52 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/20/t129284837076tbf464wijjhbo.htm/, Retrieved Fri, 03 May 2024 17:17:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112877, Retrieved Fri, 03 May 2024 17:17:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact109
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Central Tendency] [Time needed to su...] [2010-09-25 09:42:08] [b98453cac15ba1066b407e146608df68]
-    D    [Central Tendency] [Central Tendency ...] [2010-12-20 12:30:52] [47bfda5353cd53c1cf7ea7aa9038654a] [Current]
Feedback Forum

Post a new message
Dataseries X:
11,04
11,02
11,03
11,17
11,19
11,15
11,13
11,06
11,01
11,03
10,99
10,94
11,00
11,06
11,06
11,05
11,04
11,15
11,20
11,16
11,30
11,23
11,25
11,25
11,12
11,14
11,17
11,25
11,27
11,34
11,39
11,44
11,46
11,49
11,51
11,48
11,49
11,52
11,56
11,58
11,58
11,58
11,60
11,62
11,62
11,64
11,67
11,66
11,72
11,82
11,90
12,04
12,08
12,15
12,19
12,22
12,23
12,25
12,26
12,27
12,34
12,38
12,42
12,43
12,48
12,50
12,50
12,49
12,46
12,45
12,45
12,38
12,42




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112877&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112877&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112877&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time2 seconds
R Server'Sir Ronald Aylmer Fisher' @ 193.190.124.24







Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean11.62356164383560.0611241624629456190.163123312847
Geometric Mean11.6121339774314
Harmonic Mean11.6008588063740
Quadratic Mean11.6351273753705
Winsorized Mean ( 1 / 24 )11.62424657534250.0610215290651191190.494187107925
Winsorized Mean ( 2 / 24 )11.62424657534250.0609279204005111190.786859274536
Winsorized Mean ( 3 / 24 )11.62424657534250.0607891150384842191.222500409546
Winsorized Mean ( 4 / 24 )11.62369863013700.0605003575122194192.126114755426
Winsorized Mean ( 5 / 24 )11.62369863013700.0602750882005517192.844157962271
Winsorized Mean ( 6 / 24 )11.62369863013700.0602750882005517192.844157962271
Winsorized Mean ( 7 / 24 )11.62273972602740.059782157899487194.418203263404
Winsorized Mean ( 8 / 24 )11.62164383561640.0595774101212157195.067959684235
Winsorized Mean ( 9 / 24 )11.62287671232880.0594112666864351195.634218231246
Winsorized Mean ( 10 / 24 )11.61876712328770.0582200286445165199.566496166298
Winsorized Mean ( 11 / 24 )11.61876712328770.0582200286445165199.566496166298
Winsorized Mean ( 12 / 24 )11.61219178082190.0570402160511261203.579028705181
Winsorized Mean ( 13 / 24 )11.61041095890410.0534663859593644217.153464753130
Winsorized Mean ( 14 / 24 )11.61041095890410.0528954046581403219.497535446443
Winsorized Mean ( 15 / 24 )11.61041095890410.0522876361419136222.048878388619
Winsorized Mean ( 16 / 24 )11.60821917808220.0512731153891643226.399724104445
Winsorized Mean ( 17 / 24 )11.60589041095890.050881811458589228.095071269319
Winsorized Mean ( 18 / 24 )11.60095890410960.0493420038904838235.113250160214
Winsorized Mean ( 19 / 24 )11.59315068493150.0473043823901698245.075616658736
Winsorized Mean ( 20 / 24 )11.57397260273970.0442107945858905261.79064889355
Winsorized Mean ( 21 / 24 )11.56821917808220.0416631699289604277.660562021735
Winsorized Mean ( 22 / 24 )11.52904109589040.0348191480934834331.112095704839
Winsorized Mean ( 23 / 24 )11.51328767123290.0299123877929347384.900321262628
Winsorized Mean ( 24 / 24 )11.48698630136990.0245109587297261468.646960244717
Trimmed Mean ( 1 / 24 )11.62084507042250.0608480465402259190.981399258892
Trimmed Mean ( 2 / 24 )11.61724637681160.0605980017825082191.710057016516
Trimmed Mean ( 3 / 24 )11.61343283582090.0603133504038934192.551611841335
Trimmed Mean ( 4 / 24 )11.60938461538460.0599875295226004193.529967107760
Trimmed Mean ( 5 / 24 )11.60523809523810.0596494526494181194.557327515583
Trimmed Mean ( 6 / 24 )11.60081967213110.0592578394352488195.768522489035
Trimmed Mean ( 7 / 24 )11.59610169491530.0587314848644785197.442678687130
Trimmed Mean ( 8 / 24 )11.59122807017540.0581616181043496199.293424907458
Trimmed Mean ( 9 / 24 )11.58618181818180.0574593933086668201.641213925491
Trimmed Mean ( 10 / 24 )11.58056603773580.0565752226010766204.693247420214
Trimmed Mean ( 11 / 24 )11.57509803921570.0556941032884055207.833457328065
Trimmed Mean ( 12 / 24 )11.56918367346940.0545340784164587212.145946340550
Trimmed Mean ( 13 / 24 )11.56361702127660.0532908046002427216.99085063587
Trimmed Mean ( 14 / 24 )11.55777777777780.0524287769783286220.447213227102
Trimmed Mean ( 15 / 24 )11.55139534883720.0513640960684935224.892409932291
Trimmed Mean ( 16 / 24 )11.54439024390240.0500329754438691230.735632679968
Trimmed Mean ( 17 / 24 )11.53692307692310.048441505616749238.161942533308
Trimmed Mean ( 18 / 24 )11.52891891891890.0463288671510438248.849575391769
Trimmed Mean ( 19 / 24 )11.52057142857140.0438042683487606263.001115253130
Trimmed Mean ( 20 / 24 )11.51212121212120.0408474563758666281.832021709992
Trimmed Mean ( 21 / 24 )11.50483870967740.0376853725587361305.286585444952
Trimmed Mean ( 22 / 24 )11.49724137931030.0339076424233591339.075221914864
Trimmed Mean ( 23 / 24 )11.49333333333330.0311827624235678368.579703658542
Trimmed Mean ( 24 / 24 )11.49080.0290512191367821395.535896304309
Median11.51
Midrange11.72
Midmean - Weighted Average at Xnp11.5105555555556
Midmean - Weighted Average at X(n+1)p11.5289189189189
Midmean - Empirical Distribution Function11.5289189189189
Midmean - Empirical Distribution Function - Averaging11.5289189189189
Midmean - Empirical Distribution Function - Interpolation11.5289189189189
Midmean - Closest Observation11.5094871794872
Midmean - True Basic - Statistics Graphics Toolkit11.5289189189189
Midmean - MS Excel (old versions)11.5289189189189
Number of observations73

\begin{tabular}{lllllllll}
\hline
Central Tendency - Ungrouped Data \tabularnewline
Measure & Value & S.E. & Value/S.E. \tabularnewline
Arithmetic Mean & 11.6235616438356 & 0.0611241624629456 & 190.163123312847 \tabularnewline
Geometric Mean & 11.6121339774314 &  &  \tabularnewline
Harmonic Mean & 11.6008588063740 &  &  \tabularnewline
Quadratic Mean & 11.6351273753705 &  &  \tabularnewline
Winsorized Mean ( 1 / 24 ) & 11.6242465753425 & 0.0610215290651191 & 190.494187107925 \tabularnewline
Winsorized Mean ( 2 / 24 ) & 11.6242465753425 & 0.0609279204005111 & 190.786859274536 \tabularnewline
Winsorized Mean ( 3 / 24 ) & 11.6242465753425 & 0.0607891150384842 & 191.222500409546 \tabularnewline
Winsorized Mean ( 4 / 24 ) & 11.6236986301370 & 0.0605003575122194 & 192.126114755426 \tabularnewline
Winsorized Mean ( 5 / 24 ) & 11.6236986301370 & 0.0602750882005517 & 192.844157962271 \tabularnewline
Winsorized Mean ( 6 / 24 ) & 11.6236986301370 & 0.0602750882005517 & 192.844157962271 \tabularnewline
Winsorized Mean ( 7 / 24 ) & 11.6227397260274 & 0.059782157899487 & 194.418203263404 \tabularnewline
Winsorized Mean ( 8 / 24 ) & 11.6216438356164 & 0.0595774101212157 & 195.067959684235 \tabularnewline
Winsorized Mean ( 9 / 24 ) & 11.6228767123288 & 0.0594112666864351 & 195.634218231246 \tabularnewline
Winsorized Mean ( 10 / 24 ) & 11.6187671232877 & 0.0582200286445165 & 199.566496166298 \tabularnewline
Winsorized Mean ( 11 / 24 ) & 11.6187671232877 & 0.0582200286445165 & 199.566496166298 \tabularnewline
Winsorized Mean ( 12 / 24 ) & 11.6121917808219 & 0.0570402160511261 & 203.579028705181 \tabularnewline
Winsorized Mean ( 13 / 24 ) & 11.6104109589041 & 0.0534663859593644 & 217.153464753130 \tabularnewline
Winsorized Mean ( 14 / 24 ) & 11.6104109589041 & 0.0528954046581403 & 219.497535446443 \tabularnewline
Winsorized Mean ( 15 / 24 ) & 11.6104109589041 & 0.0522876361419136 & 222.048878388619 \tabularnewline
Winsorized Mean ( 16 / 24 ) & 11.6082191780822 & 0.0512731153891643 & 226.399724104445 \tabularnewline
Winsorized Mean ( 17 / 24 ) & 11.6058904109589 & 0.050881811458589 & 228.095071269319 \tabularnewline
Winsorized Mean ( 18 / 24 ) & 11.6009589041096 & 0.0493420038904838 & 235.113250160214 \tabularnewline
Winsorized Mean ( 19 / 24 ) & 11.5931506849315 & 0.0473043823901698 & 245.075616658736 \tabularnewline
Winsorized Mean ( 20 / 24 ) & 11.5739726027397 & 0.0442107945858905 & 261.79064889355 \tabularnewline
Winsorized Mean ( 21 / 24 ) & 11.5682191780822 & 0.0416631699289604 & 277.660562021735 \tabularnewline
Winsorized Mean ( 22 / 24 ) & 11.5290410958904 & 0.0348191480934834 & 331.112095704839 \tabularnewline
Winsorized Mean ( 23 / 24 ) & 11.5132876712329 & 0.0299123877929347 & 384.900321262628 \tabularnewline
Winsorized Mean ( 24 / 24 ) & 11.4869863013699 & 0.0245109587297261 & 468.646960244717 \tabularnewline
Trimmed Mean ( 1 / 24 ) & 11.6208450704225 & 0.0608480465402259 & 190.981399258892 \tabularnewline
Trimmed Mean ( 2 / 24 ) & 11.6172463768116 & 0.0605980017825082 & 191.710057016516 \tabularnewline
Trimmed Mean ( 3 / 24 ) & 11.6134328358209 & 0.0603133504038934 & 192.551611841335 \tabularnewline
Trimmed Mean ( 4 / 24 ) & 11.6093846153846 & 0.0599875295226004 & 193.529967107760 \tabularnewline
Trimmed Mean ( 5 / 24 ) & 11.6052380952381 & 0.0596494526494181 & 194.557327515583 \tabularnewline
Trimmed Mean ( 6 / 24 ) & 11.6008196721311 & 0.0592578394352488 & 195.768522489035 \tabularnewline
Trimmed Mean ( 7 / 24 ) & 11.5961016949153 & 0.0587314848644785 & 197.442678687130 \tabularnewline
Trimmed Mean ( 8 / 24 ) & 11.5912280701754 & 0.0581616181043496 & 199.293424907458 \tabularnewline
Trimmed Mean ( 9 / 24 ) & 11.5861818181818 & 0.0574593933086668 & 201.641213925491 \tabularnewline
Trimmed Mean ( 10 / 24 ) & 11.5805660377358 & 0.0565752226010766 & 204.693247420214 \tabularnewline
Trimmed Mean ( 11 / 24 ) & 11.5750980392157 & 0.0556941032884055 & 207.833457328065 \tabularnewline
Trimmed Mean ( 12 / 24 ) & 11.5691836734694 & 0.0545340784164587 & 212.145946340550 \tabularnewline
Trimmed Mean ( 13 / 24 ) & 11.5636170212766 & 0.0532908046002427 & 216.99085063587 \tabularnewline
Trimmed Mean ( 14 / 24 ) & 11.5577777777778 & 0.0524287769783286 & 220.447213227102 \tabularnewline
Trimmed Mean ( 15 / 24 ) & 11.5513953488372 & 0.0513640960684935 & 224.892409932291 \tabularnewline
Trimmed Mean ( 16 / 24 ) & 11.5443902439024 & 0.0500329754438691 & 230.735632679968 \tabularnewline
Trimmed Mean ( 17 / 24 ) & 11.5369230769231 & 0.048441505616749 & 238.161942533308 \tabularnewline
Trimmed Mean ( 18 / 24 ) & 11.5289189189189 & 0.0463288671510438 & 248.849575391769 \tabularnewline
Trimmed Mean ( 19 / 24 ) & 11.5205714285714 & 0.0438042683487606 & 263.001115253130 \tabularnewline
Trimmed Mean ( 20 / 24 ) & 11.5121212121212 & 0.0408474563758666 & 281.832021709992 \tabularnewline
Trimmed Mean ( 21 / 24 ) & 11.5048387096774 & 0.0376853725587361 & 305.286585444952 \tabularnewline
Trimmed Mean ( 22 / 24 ) & 11.4972413793103 & 0.0339076424233591 & 339.075221914864 \tabularnewline
Trimmed Mean ( 23 / 24 ) & 11.4933333333333 & 0.0311827624235678 & 368.579703658542 \tabularnewline
Trimmed Mean ( 24 / 24 ) & 11.4908 & 0.0290512191367821 & 395.535896304309 \tabularnewline
Median & 11.51 &  &  \tabularnewline
Midrange & 11.72 &  &  \tabularnewline
Midmean - Weighted Average at Xnp & 11.5105555555556 &  &  \tabularnewline
Midmean - Weighted Average at X(n+1)p & 11.5289189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function & 11.5289189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Averaging & 11.5289189189189 &  &  \tabularnewline
Midmean - Empirical Distribution Function - Interpolation & 11.5289189189189 &  &  \tabularnewline
Midmean - Closest Observation & 11.5094871794872 &  &  \tabularnewline
Midmean - True Basic - Statistics Graphics Toolkit & 11.5289189189189 &  &  \tabularnewline
Midmean - MS Excel (old versions) & 11.5289189189189 &  &  \tabularnewline
Number of observations & 73 &  &  \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112877&T=1

[TABLE]
[ROW][C]Central Tendency - Ungrouped Data[/C][/ROW]
[ROW][C]Measure[/C][C]Value[/C][C]S.E.[/C][C]Value/S.E.[/C][/ROW]
[ROW][C]Arithmetic Mean[/C][C]11.6235616438356[/C][C]0.0611241624629456[/C][C]190.163123312847[/C][/ROW]
[ROW][C]Geometric Mean[/C][C]11.6121339774314[/C][C][/C][C][/C][/ROW]
[ROW][C]Harmonic Mean[/C][C]11.6008588063740[/C][C][/C][C][/C][/ROW]
[ROW][C]Quadratic Mean[/C][C]11.6351273753705[/C][C][/C][C][/C][/ROW]
[ROW][C]Winsorized Mean ( 1 / 24 )[/C][C]11.6242465753425[/C][C]0.0610215290651191[/C][C]190.494187107925[/C][/ROW]
[ROW][C]Winsorized Mean ( 2 / 24 )[/C][C]11.6242465753425[/C][C]0.0609279204005111[/C][C]190.786859274536[/C][/ROW]
[ROW][C]Winsorized Mean ( 3 / 24 )[/C][C]11.6242465753425[/C][C]0.0607891150384842[/C][C]191.222500409546[/C][/ROW]
[ROW][C]Winsorized Mean ( 4 / 24 )[/C][C]11.6236986301370[/C][C]0.0605003575122194[/C][C]192.126114755426[/C][/ROW]
[ROW][C]Winsorized Mean ( 5 / 24 )[/C][C]11.6236986301370[/C][C]0.0602750882005517[/C][C]192.844157962271[/C][/ROW]
[ROW][C]Winsorized Mean ( 6 / 24 )[/C][C]11.6236986301370[/C][C]0.0602750882005517[/C][C]192.844157962271[/C][/ROW]
[ROW][C]Winsorized Mean ( 7 / 24 )[/C][C]11.6227397260274[/C][C]0.059782157899487[/C][C]194.418203263404[/C][/ROW]
[ROW][C]Winsorized Mean ( 8 / 24 )[/C][C]11.6216438356164[/C][C]0.0595774101212157[/C][C]195.067959684235[/C][/ROW]
[ROW][C]Winsorized Mean ( 9 / 24 )[/C][C]11.6228767123288[/C][C]0.0594112666864351[/C][C]195.634218231246[/C][/ROW]
[ROW][C]Winsorized Mean ( 10 / 24 )[/C][C]11.6187671232877[/C][C]0.0582200286445165[/C][C]199.566496166298[/C][/ROW]
[ROW][C]Winsorized Mean ( 11 / 24 )[/C][C]11.6187671232877[/C][C]0.0582200286445165[/C][C]199.566496166298[/C][/ROW]
[ROW][C]Winsorized Mean ( 12 / 24 )[/C][C]11.6121917808219[/C][C]0.0570402160511261[/C][C]203.579028705181[/C][/ROW]
[ROW][C]Winsorized Mean ( 13 / 24 )[/C][C]11.6104109589041[/C][C]0.0534663859593644[/C][C]217.153464753130[/C][/ROW]
[ROW][C]Winsorized Mean ( 14 / 24 )[/C][C]11.6104109589041[/C][C]0.0528954046581403[/C][C]219.497535446443[/C][/ROW]
[ROW][C]Winsorized Mean ( 15 / 24 )[/C][C]11.6104109589041[/C][C]0.0522876361419136[/C][C]222.048878388619[/C][/ROW]
[ROW][C]Winsorized Mean ( 16 / 24 )[/C][C]11.6082191780822[/C][C]0.0512731153891643[/C][C]226.399724104445[/C][/ROW]
[ROW][C]Winsorized Mean ( 17 / 24 )[/C][C]11.6058904109589[/C][C]0.050881811458589[/C][C]228.095071269319[/C][/ROW]
[ROW][C]Winsorized Mean ( 18 / 24 )[/C][C]11.6009589041096[/C][C]0.0493420038904838[/C][C]235.113250160214[/C][/ROW]
[ROW][C]Winsorized Mean ( 19 / 24 )[/C][C]11.5931506849315[/C][C]0.0473043823901698[/C][C]245.075616658736[/C][/ROW]
[ROW][C]Winsorized Mean ( 20 / 24 )[/C][C]11.5739726027397[/C][C]0.0442107945858905[/C][C]261.79064889355[/C][/ROW]
[ROW][C]Winsorized Mean ( 21 / 24 )[/C][C]11.5682191780822[/C][C]0.0416631699289604[/C][C]277.660562021735[/C][/ROW]
[ROW][C]Winsorized Mean ( 22 / 24 )[/C][C]11.5290410958904[/C][C]0.0348191480934834[/C][C]331.112095704839[/C][/ROW]
[ROW][C]Winsorized Mean ( 23 / 24 )[/C][C]11.5132876712329[/C][C]0.0299123877929347[/C][C]384.900321262628[/C][/ROW]
[ROW][C]Winsorized Mean ( 24 / 24 )[/C][C]11.4869863013699[/C][C]0.0245109587297261[/C][C]468.646960244717[/C][/ROW]
[ROW][C]Trimmed Mean ( 1 / 24 )[/C][C]11.6208450704225[/C][C]0.0608480465402259[/C][C]190.981399258892[/C][/ROW]
[ROW][C]Trimmed Mean ( 2 / 24 )[/C][C]11.6172463768116[/C][C]0.0605980017825082[/C][C]191.710057016516[/C][/ROW]
[ROW][C]Trimmed Mean ( 3 / 24 )[/C][C]11.6134328358209[/C][C]0.0603133504038934[/C][C]192.551611841335[/C][/ROW]
[ROW][C]Trimmed Mean ( 4 / 24 )[/C][C]11.6093846153846[/C][C]0.0599875295226004[/C][C]193.529967107760[/C][/ROW]
[ROW][C]Trimmed Mean ( 5 / 24 )[/C][C]11.6052380952381[/C][C]0.0596494526494181[/C][C]194.557327515583[/C][/ROW]
[ROW][C]Trimmed Mean ( 6 / 24 )[/C][C]11.6008196721311[/C][C]0.0592578394352488[/C][C]195.768522489035[/C][/ROW]
[ROW][C]Trimmed Mean ( 7 / 24 )[/C][C]11.5961016949153[/C][C]0.0587314848644785[/C][C]197.442678687130[/C][/ROW]
[ROW][C]Trimmed Mean ( 8 / 24 )[/C][C]11.5912280701754[/C][C]0.0581616181043496[/C][C]199.293424907458[/C][/ROW]
[ROW][C]Trimmed Mean ( 9 / 24 )[/C][C]11.5861818181818[/C][C]0.0574593933086668[/C][C]201.641213925491[/C][/ROW]
[ROW][C]Trimmed Mean ( 10 / 24 )[/C][C]11.5805660377358[/C][C]0.0565752226010766[/C][C]204.693247420214[/C][/ROW]
[ROW][C]Trimmed Mean ( 11 / 24 )[/C][C]11.5750980392157[/C][C]0.0556941032884055[/C][C]207.833457328065[/C][/ROW]
[ROW][C]Trimmed Mean ( 12 / 24 )[/C][C]11.5691836734694[/C][C]0.0545340784164587[/C][C]212.145946340550[/C][/ROW]
[ROW][C]Trimmed Mean ( 13 / 24 )[/C][C]11.5636170212766[/C][C]0.0532908046002427[/C][C]216.99085063587[/C][/ROW]
[ROW][C]Trimmed Mean ( 14 / 24 )[/C][C]11.5577777777778[/C][C]0.0524287769783286[/C][C]220.447213227102[/C][/ROW]
[ROW][C]Trimmed Mean ( 15 / 24 )[/C][C]11.5513953488372[/C][C]0.0513640960684935[/C][C]224.892409932291[/C][/ROW]
[ROW][C]Trimmed Mean ( 16 / 24 )[/C][C]11.5443902439024[/C][C]0.0500329754438691[/C][C]230.735632679968[/C][/ROW]
[ROW][C]Trimmed Mean ( 17 / 24 )[/C][C]11.5369230769231[/C][C]0.048441505616749[/C][C]238.161942533308[/C][/ROW]
[ROW][C]Trimmed Mean ( 18 / 24 )[/C][C]11.5289189189189[/C][C]0.0463288671510438[/C][C]248.849575391769[/C][/ROW]
[ROW][C]Trimmed Mean ( 19 / 24 )[/C][C]11.5205714285714[/C][C]0.0438042683487606[/C][C]263.001115253130[/C][/ROW]
[ROW][C]Trimmed Mean ( 20 / 24 )[/C][C]11.5121212121212[/C][C]0.0408474563758666[/C][C]281.832021709992[/C][/ROW]
[ROW][C]Trimmed Mean ( 21 / 24 )[/C][C]11.5048387096774[/C][C]0.0376853725587361[/C][C]305.286585444952[/C][/ROW]
[ROW][C]Trimmed Mean ( 22 / 24 )[/C][C]11.4972413793103[/C][C]0.0339076424233591[/C][C]339.075221914864[/C][/ROW]
[ROW][C]Trimmed Mean ( 23 / 24 )[/C][C]11.4933333333333[/C][C]0.0311827624235678[/C][C]368.579703658542[/C][/ROW]
[ROW][C]Trimmed Mean ( 24 / 24 )[/C][C]11.4908[/C][C]0.0290512191367821[/C][C]395.535896304309[/C][/ROW]
[ROW][C]Median[/C][C]11.51[/C][C][/C][C][/C][/ROW]
[ROW][C]Midrange[/C][C]11.72[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at Xnp[/C][C]11.5105555555556[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Weighted Average at X(n+1)p[/C][C]11.5289189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function[/C][C]11.5289189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Averaging[/C][C]11.5289189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Empirical Distribution Function - Interpolation[/C][C]11.5289189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - Closest Observation[/C][C]11.5094871794872[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - True Basic - Statistics Graphics Toolkit[/C][C]11.5289189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Midmean - MS Excel (old versions)[/C][C]11.5289189189189[/C][C][/C][C][/C][/ROW]
[ROW][C]Number of observations[/C][C]73[/C][C][/C][C][/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112877&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112877&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Central Tendency - Ungrouped Data
MeasureValueS.E.Value/S.E.
Arithmetic Mean11.62356164383560.0611241624629456190.163123312847
Geometric Mean11.6121339774314
Harmonic Mean11.6008588063740
Quadratic Mean11.6351273753705
Winsorized Mean ( 1 / 24 )11.62424657534250.0610215290651191190.494187107925
Winsorized Mean ( 2 / 24 )11.62424657534250.0609279204005111190.786859274536
Winsorized Mean ( 3 / 24 )11.62424657534250.0607891150384842191.222500409546
Winsorized Mean ( 4 / 24 )11.62369863013700.0605003575122194192.126114755426
Winsorized Mean ( 5 / 24 )11.62369863013700.0602750882005517192.844157962271
Winsorized Mean ( 6 / 24 )11.62369863013700.0602750882005517192.844157962271
Winsorized Mean ( 7 / 24 )11.62273972602740.059782157899487194.418203263404
Winsorized Mean ( 8 / 24 )11.62164383561640.0595774101212157195.067959684235
Winsorized Mean ( 9 / 24 )11.62287671232880.0594112666864351195.634218231246
Winsorized Mean ( 10 / 24 )11.61876712328770.0582200286445165199.566496166298
Winsorized Mean ( 11 / 24 )11.61876712328770.0582200286445165199.566496166298
Winsorized Mean ( 12 / 24 )11.61219178082190.0570402160511261203.579028705181
Winsorized Mean ( 13 / 24 )11.61041095890410.0534663859593644217.153464753130
Winsorized Mean ( 14 / 24 )11.61041095890410.0528954046581403219.497535446443
Winsorized Mean ( 15 / 24 )11.61041095890410.0522876361419136222.048878388619
Winsorized Mean ( 16 / 24 )11.60821917808220.0512731153891643226.399724104445
Winsorized Mean ( 17 / 24 )11.60589041095890.050881811458589228.095071269319
Winsorized Mean ( 18 / 24 )11.60095890410960.0493420038904838235.113250160214
Winsorized Mean ( 19 / 24 )11.59315068493150.0473043823901698245.075616658736
Winsorized Mean ( 20 / 24 )11.57397260273970.0442107945858905261.79064889355
Winsorized Mean ( 21 / 24 )11.56821917808220.0416631699289604277.660562021735
Winsorized Mean ( 22 / 24 )11.52904109589040.0348191480934834331.112095704839
Winsorized Mean ( 23 / 24 )11.51328767123290.0299123877929347384.900321262628
Winsorized Mean ( 24 / 24 )11.48698630136990.0245109587297261468.646960244717
Trimmed Mean ( 1 / 24 )11.62084507042250.0608480465402259190.981399258892
Trimmed Mean ( 2 / 24 )11.61724637681160.0605980017825082191.710057016516
Trimmed Mean ( 3 / 24 )11.61343283582090.0603133504038934192.551611841335
Trimmed Mean ( 4 / 24 )11.60938461538460.0599875295226004193.529967107760
Trimmed Mean ( 5 / 24 )11.60523809523810.0596494526494181194.557327515583
Trimmed Mean ( 6 / 24 )11.60081967213110.0592578394352488195.768522489035
Trimmed Mean ( 7 / 24 )11.59610169491530.0587314848644785197.442678687130
Trimmed Mean ( 8 / 24 )11.59122807017540.0581616181043496199.293424907458
Trimmed Mean ( 9 / 24 )11.58618181818180.0574593933086668201.641213925491
Trimmed Mean ( 10 / 24 )11.58056603773580.0565752226010766204.693247420214
Trimmed Mean ( 11 / 24 )11.57509803921570.0556941032884055207.833457328065
Trimmed Mean ( 12 / 24 )11.56918367346940.0545340784164587212.145946340550
Trimmed Mean ( 13 / 24 )11.56361702127660.0532908046002427216.99085063587
Trimmed Mean ( 14 / 24 )11.55777777777780.0524287769783286220.447213227102
Trimmed Mean ( 15 / 24 )11.55139534883720.0513640960684935224.892409932291
Trimmed Mean ( 16 / 24 )11.54439024390240.0500329754438691230.735632679968
Trimmed Mean ( 17 / 24 )11.53692307692310.048441505616749238.161942533308
Trimmed Mean ( 18 / 24 )11.52891891891890.0463288671510438248.849575391769
Trimmed Mean ( 19 / 24 )11.52057142857140.0438042683487606263.001115253130
Trimmed Mean ( 20 / 24 )11.51212121212120.0408474563758666281.832021709992
Trimmed Mean ( 21 / 24 )11.50483870967740.0376853725587361305.286585444952
Trimmed Mean ( 22 / 24 )11.49724137931030.0339076424233591339.075221914864
Trimmed Mean ( 23 / 24 )11.49333333333330.0311827624235678368.579703658542
Trimmed Mean ( 24 / 24 )11.49080.0290512191367821395.535896304309
Median11.51
Midrange11.72
Midmean - Weighted Average at Xnp11.5105555555556
Midmean - Weighted Average at X(n+1)p11.5289189189189
Midmean - Empirical Distribution Function11.5289189189189
Midmean - Empirical Distribution Function - Averaging11.5289189189189
Midmean - Empirical Distribution Function - Interpolation11.5289189189189
Midmean - Closest Observation11.5094871794872
Midmean - True Basic - Statistics Graphics Toolkit11.5289189189189
Midmean - MS Excel (old versions)11.5289189189189
Number of observations73



Parameters (Session):
Parameters (R input):
R code (references can be found in the software module):
geomean <- function(x) {
return(exp(mean(log(x))))
}
harmean <- function(x) {
return(1/mean(1/x))
}
quamean <- function(x) {
return(sqrt(mean(x*x)))
}
winmean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
win <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
win[j,1] <- (j*x[j+1]+sum(x[(j+1):(n-j)])+j*x[n-j])/n
win[j,2] <- sd(c(rep(x[j+1],j),x[(j+1):(n-j)],rep(x[n-j],j)))/sqrtn
}
return(win)
}
trimean <- function(x) {
x <-sort(x[!is.na(x)])
n<-length(x)
denom <- 3
nodenom <- n/denom
if (nodenom>40) denom <- n/40
sqrtn = sqrt(n)
roundnodenom = floor(nodenom)
tri <- array(NA,dim=c(roundnodenom,2))
for (j in 1:roundnodenom) {
tri[j,1] <- mean(x,trim=j/n)
tri[j,2] <- sd(x[(j+1):(n-j)]) / sqrt(n-j*2)
}
return(tri)
}
midrange <- function(x) {
return((max(x)+min(x))/2)
}
q1 <- function(data,n,p,i,f) {
np <- n*p;
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q2 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
qvalue <- (1-f)*data[i] + f*data[i+1]
}
q3 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
q4 <- function(data,n,p,i,f) {
np <- n*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- (data[i]+data[i+1])/2
} else {
qvalue <- data[i+1]
}
}
q5 <- function(data,n,p,i,f) {
np <- (n-1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i+1]
} else {
qvalue <- data[i+1] + f*(data[i+2]-data[i+1])
}
}
q6 <- function(data,n,p,i,f) {
np <- n*p+0.5
i <<- floor(np)
f <<- np - i
qvalue <- data[i]
}
q7 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
qvalue <- f*data[i] + (1-f)*data[i+1]
}
}
q8 <- function(data,n,p,i,f) {
np <- (n+1)*p
i <<- floor(np)
f <<- np - i
if (f==0) {
qvalue <- data[i]
} else {
if (f == 0.5) {
qvalue <- (data[i]+data[i+1])/2
} else {
if (f < 0.5) {
qvalue <- data[i]
} else {
qvalue <- data[i+1]
}
}
}
}
midmean <- function(x,def) {
x <-sort(x[!is.na(x)])
n<-length(x)
if (def==1) {
qvalue1 <- q1(x,n,0.25,i,f)
qvalue3 <- q1(x,n,0.75,i,f)
}
if (def==2) {
qvalue1 <- q2(x,n,0.25,i,f)
qvalue3 <- q2(x,n,0.75,i,f)
}
if (def==3) {
qvalue1 <- q3(x,n,0.25,i,f)
qvalue3 <- q3(x,n,0.75,i,f)
}
if (def==4) {
qvalue1 <- q4(x,n,0.25,i,f)
qvalue3 <- q4(x,n,0.75,i,f)
}
if (def==5) {
qvalue1 <- q5(x,n,0.25,i,f)
qvalue3 <- q5(x,n,0.75,i,f)
}
if (def==6) {
qvalue1 <- q6(x,n,0.25,i,f)
qvalue3 <- q6(x,n,0.75,i,f)
}
if (def==7) {
qvalue1 <- q7(x,n,0.25,i,f)
qvalue3 <- q7(x,n,0.75,i,f)
}
if (def==8) {
qvalue1 <- q8(x,n,0.25,i,f)
qvalue3 <- q8(x,n,0.75,i,f)
}
midm <- 0
myn <- 0
roundno4 <- round(n/4)
round3no4 <- round(3*n/4)
for (i in 1:n) {
if ((x[i]>=qvalue1) & (x[i]<=qvalue3)){
midm = midm + x[i]
myn = myn + 1
}
}
midm = midm / myn
return(midm)
}
(arm <- mean(x))
sqrtn <- sqrt(length(x))
(armse <- sd(x) / sqrtn)
(armose <- arm / armse)
(geo <- geomean(x))
(har <- harmean(x))
(qua <- quamean(x))
(win <- winmean(x))
(tri <- trimean(x))
(midr <- midrange(x))
midm <- array(NA,dim=8)
for (j in 1:8) midm[j] <- midmean(x,j)
midm
bitmap(file='test1.png')
lb <- win[,1] - 2*win[,2]
ub <- win[,1] + 2*win[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(win[,1],type='b',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(win[,1],type='l',main=main, xlab='j', pch=19, ylab='Winsorized Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
bitmap(file='test2.png')
lb <- tri[,1] - 2*tri[,2]
ub <- tri[,1] + 2*tri[,2]
if ((ylimmin == '') | (ylimmax == '')) plot(tri[,1],type='b',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(min(lb),max(ub))) else plot(tri[,1],type='l',main=main, xlab='j', pch=19, ylab='Trimmed Mean(j/n)', ylim=c(ylimmin,ylimmax))
lines(ub,lty=3)
lines(lb,lty=3)
grid()
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Central Tendency - Ungrouped Data',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Measure',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.element(a,'S.E.',header=TRUE)
a<-table.element(a,'Value/S.E.',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('arithmetic_mean.htm', 'Arithmetic Mean', 'click to view the definition of the Arithmetic Mean'),header=TRUE)
a<-table.element(a,arm)
a<-table.element(a,hyperlink('arithmetic_mean_standard_error.htm', armse, 'click to view the definition of the Standard Error of the Arithmetic Mean'))
a<-table.element(a,armose)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('geometric_mean.htm', 'Geometric Mean', 'click to view the definition of the Geometric Mean'),header=TRUE)
a<-table.element(a,geo)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('harmonic_mean.htm', 'Harmonic Mean', 'click to view the definition of the Harmonic Mean'),header=TRUE)
a<-table.element(a,har)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('quadratic_mean.htm', 'Quadratic Mean', 'click to view the definition of the Quadratic Mean'),header=TRUE)
a<-table.element(a,qua)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
for (j in 1:length(win[,1])) {
a<-table.row.start(a)
mylabel <- paste('Winsorized Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(win[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('winsorized_mean.htm', mylabel, 'click to view the definition of the Winsorized Mean'),header=TRUE)
a<-table.element(a,win[j,1])
a<-table.element(a,win[j,2])
a<-table.element(a,win[j,1]/win[j,2])
a<-table.row.end(a)
}
for (j in 1:length(tri[,1])) {
a<-table.row.start(a)
mylabel <- paste('Trimmed Mean (',j)
mylabel <- paste(mylabel,'/')
mylabel <- paste(mylabel,length(tri[,1]))
mylabel <- paste(mylabel,')')
a<-table.element(a,hyperlink('arithmetic_mean.htm', mylabel, 'click to view the definition of the Trimmed Mean'),header=TRUE)
a<-table.element(a,tri[j,1])
a<-table.element(a,tri[j,2])
a<-table.element(a,tri[j,1]/tri[j,2])
a<-table.row.end(a)
}
a<-table.row.start(a)
a<-table.element(a,hyperlink('median_1.htm', 'Median', 'click to view the definition of the Median'),header=TRUE)
a<-table.element(a,median(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,hyperlink('midrange.htm', 'Midrange', 'click to view the definition of the Midrange'),header=TRUE)
a<-table.element(a,midr)
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_1.htm','Weighted Average at Xnp',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[1])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_2.htm','Weighted Average at X(n+1)p',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[2])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_3.htm','Empirical Distribution Function',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[3])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_4.htm','Empirical Distribution Function - Averaging',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[4])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_5.htm','Empirical Distribution Function - Interpolation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[5])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_6.htm','Closest Observation',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[6])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_7.htm','True Basic - Statistics Graphics Toolkit',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[7])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
mymid <- hyperlink('midmean.htm', 'Midmean', 'click to view the definition of the Midmean')
mylabel <- paste(mymid,hyperlink('method_8.htm','MS Excel (old versions)',''),sep=' - ')
a<-table.element(a,mylabel,header=TRUE)
a<-table.element(a,midm[8])
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Number of observations',header=TRUE)
a<-table.element(a,length(x))
a<-table.element(a,'')
a<-table.element(a,'')
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')